The Yellow Jackets (15-16, 6-12 Atlantic Coast Conference) have won two straight after ending a four-game skid with an upset victory at No. 7 Syracuse on Tuesday.
Joey van Zegeren finished with a career-high 21 points and seven rebounds for Virginia Tech (9-12, 2-16), which has dropped six in a row and 16 of 17.
Coming off the 67-62 win over Syracuse - the most illustrious victory in coach Brian Gregory's three-year tenure - Georgia Tech never trailed after Golden's 3-pointer made it 19-18 with 3:40 left in the first half.
Even so, the Jackets began the day in 13th in the 15-team ACC and are likely to miss the NCAA tournament and the NIT for the fourth straight year. They have a 16-36 league record under Gregory.
Injuries and inconsistency have hurt Georgia Tech and Virginia Tech all season.
Virginia Tech, under second-year coach James Johnson, finished last in the league for the second straight season.
Carter scored from the left baseline and hit a jumper on consecutive possessions as the Jackets went up by 16.
Johnson sought to calm down the Hokies, calling a timeout with 12:40 remaining. But after Marshall Wood hit a 3 from the left wing for Virginia Tech, Johnson followed with another 30-second timeout 2 minutes later with the Hokies trailing 50-33.
Virginia Tech had a shot clock violation on the ensuing possession, and Carter hit a 19-footer to make it 52-33.
Miller, who had a game-high nine rebounds, hit his first six shots from the field.
The Hokies missed 19 of their first 26 shots before van Zegeren's layup cut the lead to 25-20 in the final minute of the first half.
Jarell Eddie and Devin Wilson, Virginia Tech's two leading scorers this season, were a combined 4 for 18 from the field.